Step 1

Arrange 2 racks to divide the oven into thirds and heat the oven to 400ºF. Place 2 1/2 pounds sliced Yukon Gold potatoes on a rimmed baking sheet. Drizzle with 1 of the tablespoon olive oil and season with 1 teaspoon of the kosher salt and a few grinds of black pepper. Toss to coat and arrange into a single layer. Repeat tossing and arranging 2 1/2 pounds sliced eggplant, 1 tablespoon olive oil, 1 teaspoon kosher salt, and black pepper together on a second baking sheet.

Step 2

Bake the eggplant on the upper rack and the potatoes on the lower rack for 20 minutes. Flip the eggplant and potato slices, return to the oven onto the same racks, and bake until lightly browned, 15 to 20 minutes more. Meanwhile, make the meat filling.

Step 3

Heat 2 tablespoons olive oil in a pot or Dutch oven over medium heat until shimmering. Add 1 pound ground beef, 1 teaspoon of the kosher salt, and a few grinds of black pepper. Cook, breaking up the meat into small pieces, until browned and cooked through, 5 to 7 minutes. Using a slotted spoon, transfer to a large bowl.

Step 4

Add 1 pound ground lamb, 1 teaspoon of the kosher salt, and a few grinds of black pepper. Repeat cooking the meat and transferring to the bowl.

Step 5

Add 2 diced medium sweet onions, 6 minced garlic cloves, 1 tablespoon coarsely chopped fresh parsley leaves if using, 1 tablespoon coarsely chopped fresh oregano leaves, and the remaining 1/2 teaspoon kosher salt to the pot. Cook, stirring occasionally and scraping up any browned bits from the bottom, until the vegetables are translucent and fragrant, about 5 minutes.

Step 6

Make a well in the center of the vegetables. Add 1/4 cup tomato paste into the well and let cook undisturbed for 1 minute. Stir into the vegetables. Stir in 1 cup dry white wine and cook until mostly evaporated, 3 to 5 minutes.

Step 7

Return the meats and any accumulated juices to the pot. Add 1 (28-ounce) can crushed tomatoes, 2 dried bay leaves, 2 whole cloves, and 1 halved (3-inch) cinnamon stick. Stir to combine and bring to a simmer over medium-high heat.

Step 8

Reduce the heat to low and cook, stirring occasionally, until the sauce is darkened in color, thickened, and the tomatoes are no longer acidic and the flavors meld, 30 to 40 minutes. Taste and season with more kosher salt as needed. Meanwhile, make the béchamel sauce.

Step 9

Melt 1 stick unsalted butter in a medium saucepan over medium heat. Whisk in 2/3 cup all-purpose flour and cook, whisking often, for about 1 1/2 minutes to cook the floury taste out.

Step 10

While constantly whisking, slowly pour in 4 cups whole milk. Whisk until smooth and cook, whisking often, until simmering. Reduce the heat to medium-low and cook, whisking often, until thickened enough to coat the back of a spoon, about 5 minutes.

Step 11

Whisk in 1/2 cup of the grated Pecorino Romano cheese, 1/2 teaspoon kosher salt, 1/2 teaspoon freshly grated nutmeg, and 1/4 teaspoon black pepper. Taste and season with more kosher salt as needed. Transfer to a heatproof bowl and cover tightly with plastic wrap. Let cool for about 20 minutes. Uncover and whisk in 4 large egg yolks. Cover again.

Step 12

Reduce the oven temperature to 375ºF.

Step 13

Taste the potatoes and eggplant and season with kosher salt as needed — they should be well seasoned. Arrange the potato slices in a broiler-safe 9x13-inch baking dish in an even layer. They can overlap. Layer the eggplant on top of the potatoes. Use your hands and press down on the vegetables to compact slightly.

Step 14

Remove the cinnamon stick pieces, bay leaves, and cloves from the meat sauce and discard. Spread the meat sauce evenly over the vegetables. Dollop the béchamel sauce over the meat sauce and spread into an even layer. Sprinkle with the remaining 1/2 cup grated Pecorino Romano.

Step 15

Bake until the top is browned, about 45 minutes. If you’d like the top to be more deeply browned, turn on the broiler and broil as needed. Let cool for at least 30 minutes before serving so the layers firm up. Garnish with more chopped parsley and oregano if desired.